For example, here is a partial proof:
Let . Clearly
case 1:
Let . Suppose . Then . On the other hand , so . Therefore, .
Do you see how this follows the definition that I gave in the top?
Now it remains to show the same, in the case

For example, here is a partial proof:
Let . Clearly
case 1:
Let . Suppose . Then . On the other hand , so . Therefore, .
Do you see how this follows the definition that I gave in the top?
Now it remains to show the same, in the case

That is a waste of effort. There is absolutely no reason to reinvent the wheel.
The object of proof at this level is to deepen understanding, not to show off.